Atomic and Molecular Spectroscopy Quiz
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Atomic and Molecular Spectroscopy Quiz

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Questions and Answers

What does the absorption spectrum represent?

  • Energy transitions from the ground state to the excited state (correct)
  • Energy transitions from the excited state to the ground state
  • Energy levels that cannot be quantified
  • Energy emissions from molecules in the ground state

    • What is the main difference between atomic and molecular spectroscopy?

  • Molecular spectroscopy considers rotational, vibrational, and electronic transitions (correct)
  • Atomic spectroscopy results in a continuous spectrum
  • Molecular spectroscopy is simpler than atomic spectroscopy
  • Atomic spectroscopy involves only vibrational transitions

    • Which of the following correctly defines the energy difference ΔE when a photon is absorbed?

  • ΔE = E<sub>0</sub> + E<sub>1</sub>
  • ΔE = E<sub>1</sub> / E<sub>0</sub>
  • ΔE = E<sub>1</sub> – E<sub>0</sub> (correct)
  • ΔE = λh

    • Which constant is used to determine the energy of a photon?

    <p>Planck's constant</p> Signup and view all the answers

    Which phenomenon occurs when a molecule emits energy?

    <p>Spontaneous emission</p> Signup and view all the answers

    What type of spectrum do atoms produce?

    <p>A characteristic line spectrum</p> Signup and view all the answers

    What does the term 'molecular spectroscopy' refer to?

    <p>The interaction of electromagnetic radiation with molecules</p> Signup and view all the answers

    What does Planck's formula for photon energy involve?

    <p>Frequency and wavelength</p> Signup and view all the answers

    What does a change in the vibrational quantum number Δv = +1 indicate?

    <p>Absorption of energy</p> Signup and view all the answers

    Which selection rule corresponds to electronic transitions in atomic spectra?

    <p>Δl = ± 1</p> Signup and view all the answers

    What are transitions that violate the selection rules known as?

    <p>Forbidden transitions</p> Signup and view all the answers

    For rotational transitions, what is the selection rule that must be observed?

    <p>ΔJ = ± 1</p> Signup and view all the answers

    Which of the following statements is true regarding allowed transitions?

    <p>They have higher probability.</p> Signup and view all the answers

    What indicates a transition that is likely to have a very weak signal?

    <p>Forbidden transition</p> Signup and view all the answers

    What quantum number change does not allow transitions between an s-orbital and a d-orbital?

    <p>Δl = +2</p> Signup and view all the answers

    What determines the intensity and sharpness of spectral lines?

    <p>Allowed or forbidden transitions</p> Signup and view all the answers

    Which energy type in a molecule is considered negligibly small compared to the others?

    <p>Translational energy</p> Signup and view all the answers

    In the Born-Oppenheimer approximation, which energy is not included in the simplified total energy equation?

    <p>Translational energy</p> Signup and view all the answers

    Which quantum number is associated with the vibrational energy levels of an excited state electronic energy level?

    <p>v’</p> Signup and view all the answers

    What principle explains the simplification of the total energy of a molecule?

    <p>Born-Oppenheimer approximation</p> Signup and view all the answers

    Which of the following correctly orders the types of energy from largest to smallest?

    <p>E<sub>el</sub> &gt;&gt; E<sub>vib</sub> &gt;&gt; E<sub>rot</sub> &gt;&gt; E<sub>tr</sub></p> Signup and view all the answers

    Which transition leads to the formation of electronic spectra?

    <p>Electronic transitions</p> Signup and view all the answers

    What are vibrational quantum numbers used to designate?

    <p>Vibrational energy levels of electronic states</p> Signup and view all the answers

    What does the rotational energy of a diatomic molecule depend on?

    <p>Rotation about the axis through the center of gravity</p> Signup and view all the answers

    What is the defining characteristic of a sharp spectral line?

    <p>It has no width.</p> Signup and view all the answers

    How is the natural line width defined in relation to the life-time of an energy level?

    <p>Δν is inversely proportional to Δt.</p> Signup and view all the answers

    Which principle explains the natural broadening or life-time broadening of spectral lines?

    <p>Heisenberg’s uncertainty principle.</p> Signup and view all the answers

    What is the relationship between the width of a spectral line and the stability of the excited state?

    <p>Stable excited states produce sharp lines.</p> Signup and view all the answers

    What effect does collision broadening have on spectral lines?

    <p>It broadens the spectral lines.</p> Signup and view all the answers

    Which equation relates uncertainty in energy to uncertainty in time?

    <p>ΔE × Δt = h/4π.</p> Signup and view all the answers

    What is the effect of a high life-time on a spectral signal?

    <p>It leads to sharper signals.</p> Signup and view all the answers

    What determines the strength of a signal in spectral lines?

    <p>The intensity of the spectral line.</p> Signup and view all the answers

    What can be inferred when the energy difference ΔE is large according to Boltzmann's population of energy levels?

    <p>N is less than N<sub>0</sub></p> Signup and view all the answers

    Which transition is associated with a higher probability and stronger signals?

    <p>Allowed transitions</p> Signup and view all the answers

    Why is absorption spectroscopy preferred over emission spectroscopy in molecular spectroscopy?

    <p>Absorption spectra do not require heating the sample.</p> Signup and view all the answers

    What is the relationship between the ground state and the first excited state regarding spectral line intensity?

    <p>Spectral lines from E<sub>0</sub> to E<sub>1</sub> are more intense.</p> Signup and view all the answers

    What defines the line width of a spectral line?

    <p>The width at half the height of the signal.</p> Signup and view all the answers

    Which equation relates the number of molecules in the excited state with those in the ground state?

    <p>N/N<sub>0</sub> = e<sup>-ΔE/kT</sup></p> Signup and view all the answers

    What happens to the probability of a transition when selection rules are violated?

    <p>The probability decreases.</p> Signup and view all the answers

    What is the Boltzmann constant denoted as in equations?

    <p>k</p> Signup and view all the answers

    Study Notes

    Photon Energy

    • The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength.
    • The energy of a photon can be calculated using Planck's constant (h = 6.626 × 10-34 Js), the frequency (ν) of the photon, and the speed of light (c).

    Absorption and Emission Spectra

    • Molecules have quantized energy levels, meaning they can only exist in specific energy states.
    • Absorption spectrum: When a molecule absorbs electromagnetic radiation, it transitions from its ground state to an excited state. The energy of the absorbed photon is equal to the energy difference between the two states.
    • Emission spectrum: When a molecule in an excited state transitions back to its ground state, it emits a photon with energy equal to the energy difference between the states.

    Atomic and Molecular Spectroscopy

    • Atomic spectroscopy involves the study of the interactions between electromagnetic radiation and atoms.
    • The characteristic line spectrum of an atom arises from electronic transitions between energy levels.
    • Molecular spectroscopy involves the study of the interactions between electromagnetic radiation and molecules.
    • Molecular spectra are more complex than atomic spectra because molecular energy levels are influenced by electronic, vibrational, and rotational transitions.

    Molecular Energy Levels

    • According to the Born-Oppenheimer approximation, the total energy of a molecule can be separated into translational, rotational, vibrational, and electronic energy components.
    • Electronic energy levels are the highest, followed by vibrational, rotational, and translational energy levels.
    • Translational energy is not quantized and is negligible, so the total energy of a molecule can be considered as the sum of rotational, vibrational, and electronic energy.
    • Rotational energy arises from the rotation of the molecule, vibrational energy arises from the stretching and bending of chemical bonds.

    Electronic Transitions

    • Transitions between electronic energy levels correspond to ultraviolet and visible radiation, resulting in electronic spectra.
    • Absorption spectra are characteristic properties of compounds, with no two compounds having the same absorption spectrum.

    Selection Rules

    • Selection rules dictate which transitions between energy levels are allowed.
    • For vibrational transitions: Δv = ±1, where v is the vibrational quantum number.
    • For rotational transitions: ΔJ = ±1, where J is the rotational quantum number.
    • For electronic transitions in atomic spectra: Δl = ±1, where l is the azimuthal quantum number.
    • Transitions that obey selection rules are called allowed transitions, while those that violate them are called forbidden transitions.
    • Allowed transitions are more intense and stronger than forbidden transitions.

    Width and Intensities of Spectral Lines

    • The sharpness of a spectral line determines its width.
    • The strength of a spectral line determines its intensity.

    Factors Affecting Width of Spectral Lines

    • Natural broadening or life-time broadening: is due to the uncertainty principle, that the energy of a state is inversely proportional to the life-time of that state.
    • Collision broadening: collisions with other molecules lead to broadening of the spectral lines, especially in ultraviolet and visible spectra.

    Factors Affecting Intensity of Spectral Lines

    • Boltzmann population of energy levels: the number of molecules in an excited state is less than the number in the ground state according to the Boltzmann distribution.
    • Transition probability: transitions with higher probability are more intense.

    Conceptual Problems

    • The width of a spectral line is determined by the width at half the value of absorption.
    • Absorption spectra are more commonly used in molecular spectroscopy than emission spectra because they are easier to interpret and don´t require heating the sample to a high temperature.

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